In-evolution operators in genetic coalgebras

Paniello, Irene

doi:10.1016/j.laa.2020.03.032

Cited by 5 publications

(2 citation statements)

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“…Although it is not possible to include the many existing and relevant references about the subject in a few lines, we shall highlight some of them and we refer the reader to the references therein. Some of the main lines of research are focused on the study of different mathematical properties like the classification of evolution algebras [1], the characterization of their derivation spaces [2,3,6,8], and the analysis of related co-algebras [21][22][23]. Regarding connections with other fields fields, one can refer the reader to the following works [4,5,10,20,24,26].…”

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confidence: 99%

The connection between evolution algebras, random walks and graphs

2019

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Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov chains. The winning of this relation is that many results coming from Probability Theory may be stated in the context of Abstract Algebra. In this paper we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be seen as a random walk on a graph we believe that our results may add a new landscape in the study of Markov evolution algebras. ∞ k=1 c ik = 1,for any i, k, then A is called Markov evolution algebra. The name is due to that there is an interesting one-to-one correspondence between A and a discrete time Markov chain (X n ) n≥0 with 2010 Mathematics Subject Classification. 05C25, 17D92, 17D99, 05C81.

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confidence: 99%

The connection between evolution algebras, random walks and graphs

2019

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“…Petoukhov & Petukhova (2016) and Petoukhov (2017) studied the systems of structured alphabets of DNA and RNA in matrix forms of their representations. Paniello (2021) introduced the concept of in-evolutionary operator ergodicity defined on coalgebras with genetic realization. This concept provides new insights into the correspondence between genetic coalgebra and cubic stochastic matrices, the in-evolution operator emerging as a Markov process defined by the matrix accompanying coalgebra cubic stochastic matrices.…”

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confidence: 99%

An Analysis Genotype Inheritance in a Trihybrid Cross by Applying a Diagonalization of Matrix Method

Azis

Syanur

Amanto

et al. 2022

DJM

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This research aimed to find out the formulation of inheritance to know the genotype of the n-th generation in trihybrid crosses with controlled parent genotypes and analyze them by applying the diagonalization of a matrix. Matrix diagonalization makes it easier to find out the inheritance genotype of the n-th generation in trihybrid to obtain superior offspring compared with crossing it one by one, which requires a lot of time and cost. Based on the analysis, an equation for the probability of inheritance was obtained for 27 genotypes of the n-th generation, and the resulting offspring in an infinite generation are likely to have the TTKKBB genotype.

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